Related papers: Lemmings is PSPACE-complete
We introduce the following class of partizan games, called pomax games. Given a partially ordered set whose elements are colored black or white, the players Black and White take turns removing any maximal element of their own color. If…
In combinatorial game theory, the winning player for a position in normal play is analyzed and characterized via algebraic operations. Such analyses define a value for each position, called a game value. A game (ruleset) is called universal…
The Reward-Penalty-Selection Problem (RPSP) can be seen as a combination of the Set Cover Problem (SCP) and the Hitting Set Problem (HSP). Given a set of elements, a set of reward sets, and a set of penalty sets, one tries to find a subset…
We initiate the study of trembling-hand perfection in sequential (i.e., extensive-form) games with correlation. We introduce the extensive-form perfect correlated equilibrium (EFPCE) as a refinement of the classical extensive-form…
Maximal snake polyominoes are difficult to study numerically in large rectangles, as computing them requires the complete enumeration of all snakes for a specific grid size, which corresponds to a brute force algorithm. This technique is…
Large Language Models (LLMs) have gained widespread popularity across diverse domains involving text generation, summarization, and various natural language processing tasks. Despite their inherent limitations, LLM-based designs have shown…
For vertex cover games (introduced by Deng et al., Math. Oper. Res., 24:751-766, 1999), we investigate population monotonic allocation schemes (introduced by Sprumont, Games Econ. Behav., 2: 378-394, 1990). We show that the existence of a…
We define a class of zero-sum games with combinatorial structure, where the best response problem of one player is to maximize a submodular function. For example, this class includes security games played on networks, as well as the problem…
Large language models (LLMs) are known to perform well on language tasks, but struggle with reasoning tasks. This paper explores the ability of LLMs to play the 2D puzzle game Baba is You, in which players manipulate rules by rearranging…
The guarding game is a game in which several cops try to guard a region in a (directed or undirected) graph against Robber. Robber and the cops are placed on the vertices of the graph; they take turns in moving to adjacent vertices (or…
Bloxorz is an online puzzle game where players move a 1 by 1 by 2 block by tilting it on a subset of the two dimensional grid. Bloxorz features switches that open and close trapdoors. The puzzle is to move the block from its initial…
In 2010, Bre\v{s}ar, Klav\v{z}ar and Rall introduced the optimization variant of the graph domination game and the game domination number, which was proved PSPACE-hard by Bre\v{s}ar et al. in 2016. In 2024, Leo Versteegen obtained the…
In this paper we study the computational complexity of the game of Scrabble. We prove the PSPACE-completeness of a derandomized model of the game, answering an open question of Erik Demaine and Robert Hearn.
Developing autonomous agents that can strategize and cooperate with humans under information asymmetry is challenging without effective communication in natural language. We introduce a shared-control game, where two players collectively…
Evolutionary game theory studies populations that change in response to an underlying game. Often, the functional form relating outcome to player attributes or strategy is complex, preventing mathematical progress. In this work, we…
Competitive Pok\'emon Singles (CPS) is a popular strategy game where players learn to exploit their opponent based on imperfect information in battles that can last more than one hundred stochastic turns. AI research in CPS has been led by…
Game maps are useful for human players, general-game-playing agents, and data-driven procedural content generation. These maps are generally made by hand-assembling manually-created screenshots of game levels. Besides being tedious and…
Despite recent advances in multimodal large language models (MLLMs), their development has predominantly focused on English- and western-centric datasets and tasks, leaving most of the world's languages and diverse cultural contexts…
Reasoning is the fundamental capability of large language models (LLMs). Due to the rapid progress of LLMs, there are two main issues of current benchmarks: i) these benchmarks can be crushed in a short time (less than 1 year), and ii)…
We create a new two-player game on the Sperner Triangle based on Sperner's lemma. Our game has simple rules and several desirable properties. First, the game is always certain to have a winner. Second, like many other interesting games such…